Given that there are quite large variations in "performance" across the bevel boxes fitted, it's apparent that an improvement in production quality is required in the first instance.
Super-finishing the gears at the production stage isn't too expensive.
Combine this with closer attention to alignment and tolerances and there's no reason that there shouldn't be an improvement across the board.
It's a very simple gearbox, and assuming it's fit for purpose in the first instance, the problems should be easily solvable at the production stage.
It would be normal practice to include noise limits in the specification. I wonder if Morgan did so ?
Has there been any improvement on more recent cars or it still the luck of the draw whether you get a quiet one ?